[math-fun] Problem(N): Use all KxL rectangles of area <= N to tile some square.

An interesting problem -- and its solution -- appeared in the most recent American Math. Monthly: a) Given integer N > 0, let R(N) be the set of all KxL rectangles with integer sides whose area is <= N (with no two isometric). Find an N > 1 such that all the members of R(N), each used exactly once, can be used to tile a square? b) Show the analogous question in 3D has no solution: If C(N) is the set of rectangular solids with integer sides of volume <= N (with no two isometric), then for N > 1 there is no cube that can be tiled by all the members of C(N), each used exactly once. --Dan